-LRB- CNN -RRB- -- Leaders from Britain and Iran met Wednesday for the first time in 35 years , a potential breakthrough conversation that occurs at a time when Tehran is trying to shed Western-led sanctions over its nuclear program and Western nations are trying to garner international support for their campaign against ISIS .

Iranian President Hassan Rouhani acknowledged the meeting between him and British Prime Minister David Cameron with a tweet -- picture included -- from the sidelines of the United Nations General Assembly in New York .

`` 1 hour of constructive & pragmatic dialogue , new outlook #UNGA , '' read his message on the Cameron meeting .

During his U.N. speech later Wednesday , Cameron talked about the meeting , the first since the 1979 Iranian Revolution .

After talking about the need for the anti-ISIS coalition to be `` inclusive , engaging the widest possible coalition of countries as possible , '' Cameron touched on his conversation with Rouhani .

The two leaders have `` severe disagreements , '' Cameron said , pointing to `` Iran 's support for terrorist organizations , its nuclear program , its treatment of its people . All these need to change . ''

Then again , Cameron added , `` Iran 's leaders could help in defeating the threat from ISIL , '' using a commonly used acronym for ISIS , which calls itself the Islamic State .

`` They could help secure a more stable and inclusive Iraq and a more stable and inclusive Syria , '' he said . `` And if they are prepared to do this , then we should welcome their engagement . ''

Cameron 's comments came after the UK mission to the United Nations put out a statement on the meeting , saying the two leaders `` agreed that we should seek to progressively improve our bilateral relationship . ''

That statement referenced addressing `` the future of Iran 's nuclear program . '' That remains a focus in Tehran , though the hot topic this week at the United Nations is what to do about ISIS .

ISIS consists of Sunni Muslims aiming to create a vast caliphate in the region under its strict , distinct version of Sharia law . Its advances into neighboring Iraq could pose a threat to Iran , especially given that Iran is made up predominantly of Shiite Muslims .

In fact , Iranian leaders have voiced support for Iraq 's government -- which is also led by Shiites -- in its fight against the Islamic extremist organization . Brig. Gen. Amir-Ali Hajizadeh even said that members of Iran 's Islamic Revolutionary Guard `` stopped '' ISIS from entering the Kurdish city of Irbil , according to a report Wednesday from state-run Press TV .

But , in the same story , Hajizadeh ripped the U.S.-led anti-ISIS coalition as part of Washington 's `` psychological warfare '' policy .

Rouhani on Wednesday criticized the coalition airstrikes in Syria , saying they do not have `` any legal standing '' because U.N. members have n't sanctioned them . Iran has been one of the biggest allies of Syrian President Bashar al-Assad , the man who U.S. President Barack Obama and other Western leaders have publicly said they want out of power -- even going so far as to support moderate opposition elements fighting to oust him .

Rouhani used rhetorical questions to make his case on Twitter , writing , `` Was n't DAESH -LRB- #ISIS -RRB- the same group who fought the Syrian gov & the Syrian army ? How is that they were not categorised as #terrorists then ? ''

Saying that his country never `` had doubts or delays in countering #ISIS , '' Rouhani tweeted , `` Why is it that #ISIS went from not-so-bad to extremely-bad depending on who they had targeted in their #terrorist operations ? ''

Notwithstanding such criticism and the fact he did n't meet with Obama in New York , Rouhani did n't close the door to major changes in his nation 's relationship with its longstanding , often bitter rival , the United States .

`` If we are able to reach a #nuclear agreement , '' Rouhani tweeted , `` a new atmosphere would emerge in US-Iran relations , which I believe would benefit both nations . ''

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NEW : Iran President tweets on `` 1 hour of constructive & pragmatic dialogue ''

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NEW : He criticizes U.S.-led strikes in Syria , yet opens door to `` a new atmosphere '' with U.S.

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NEW : Cameron : Despite `` severe disagreements , '' Iranians could help defeat ISIS

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NEW : Prime Minister : If they can help , `` we should welcome their engagement ''